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Literature cited
V. I. Gorbachuk and M. L. Gorbachuk, “Some problems in the spectral theory of elliptic-type differential equations in a space of vector-functions on a finite interval,” Ukr. Mat. Zh.,28, No. 1, 12–26 (1976).
V. I. Gorbachuk and M. L. Gorbachuk, Boundary Problems for Differential-Operator Equations [in Russian], Naukova Dumka, Kiev (1984).
Yu. M. Berezanskii, Expansions in Eigenfunctions of Selfadjoint Operators. Translations of Math. Monographs, Vol. 17, Am. Math. Soc., Providence, Rhode Island (1968).
M. Sh. Birman and M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in Hubert Space [in Russian], Leningrad State Univ. (1970).
V. I. Gorbachuk and M. L. Gorbachuk, “On some classes of boundary problems for a Sturm-Liouville equation with operator potential,” Ukr. Mat. Zh.,24, No. 6, 726–734 (1972).
A. N. Kochubei, “Spectral properties of differential-operator equations of even order,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Kiev (1975).
A. N. Kochubei, “On extensions of symmetric operators and symmetric binary relations,” Mat. Zametki,17, No. 1, 41–48 (1975).
M. G. Krein, “Theory of self-adjoint extensions of semibounded operators and its applications. I,” Mat. Sb.,20, No. 3, 431–495 (1947).
M. Sh. Birman, “On the theory of self-adjoint extensions of positive-definite operators,” Mat. Sb.,38, No. 4, 431–450 (1956).
M. L. Gorbachuk and A. N. Kochubei, “Self-adjoint boundary problems for some classes of differential-operator equations of second order,” Dokl. Akad. Nauk SSSR,201, No. 5, 1029–1032 (1971).
M. L. Gorbachuk and V. A. Mikhailets, “Semibounded self-adjoint extensions of symmetric operators,” Dokl. Akad. Nauk SSSR,226, No. 4, 765–768 (1976).
V. I. Gorbachuk, “On asymptotics of the eigenvalues of boundary problems for differential operators in a space of vector-functions,” Ukr. Mat. Zh.,27, No. 5, 657–664 (1975).
V. A. Mikhailets, “Distribution of eigenvalues of an operator Sturm-Liouville equation,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 3, 607–619 (1977).
V. A. Mikhailets, “Spectra of operators and boundary problems,” in: Spectral Analysis of Differential Operators [in Russian], Math. Institute, Academy of Sciences of Ukr. SSR (1980), pp. 106–131.
P. L. Ul'yanov, “On series of the permuted trigonometric systems,” Izv. Akad. Nauk SSSR, Ser. Mat.,22, No. 4, 515–542 (1958).
M. A. Krasnosel'skii and E. I. Pustyl'nik, “Utilization of fractional powers of operators in the study of Fourier series in the eigenfunctions of differential operators,” Dokl. Akad. Nauk SSSR,122, No. 6, 978–981 (1958).
M. L. Gorbachuk and V. A. Kutovoi, “Some problems of spectral theory for the operator Sturm-Liouville equations on the half-axis,” in: Spectral Analysis of Differential Operators [in Russian], Math. Institute, Academy of Sciences of Ukr. SSR, Kiev (1980), pp. 67–83.
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Translated from Ukrainskii Matheraticheskii Zhurnal, Vol. 38, No. l, pp. 49–55, January–February, 1986.
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Mikhailets, V.A. Spectral analysis of elliptic differential equations in Hilbert space. Ukr Math J 38, 41–46 (1986). https://doi.org/10.1007/BF01056755
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DOI: https://doi.org/10.1007/BF01056755